Recursion operators for vacuum Einstein equations with symmetries

TL;DR

This paper derives recursion operators for the vacuum Einstein equations under specific symmetry conditions, facilitating the generation of solutions for metrics with two commuting Killing vectors orthogonal to 2D leaves.

Contribution

It introduces explicit recursion operators for the vacuum Einstein equations with symmetries, advancing solution-generating techniques in general relativity.

Findings

Derived direct and inverse recursion operators for the equations.

Applicable to metrics with two commuting orthogonal Killing vectors.

Enhances methods for constructing solutions in symmetric spacetimes.

Abstract

Direct and inverse recursion operator is derived for the vacuum Einstein equations for metrics with two commuting Killing vectors that are orthogonal to a foliation by 2-dimensional leaves.